I've noticed the "been" as well but I know there are people born and raised in the US who say it the same way. If I didn't know he was putting on an accent I'd not think it a mistake.
Totally. I had a friend called Jennifer from Boston who pronounced "been" that way, and also pronounced "ask" as "ah-sk." New Englanders occasionally have aspects of their accents that sound British.
I remember right after Schindler's List when he got famous, Ralph Fiennes did Quiz Show and Strange Days; in the former, his character was from New England so the flaws in his American accent actually didn't sound bad. In Strange Days, playing an L.A. cop, they were glaringly apparent. ;)